What Volume Is Integrated Over for Dipole Moment in Griffiths' Electrodynamics?

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SUMMARY

The dipole moment in Griffiths' "An Introduction to Electrodynamics" is defined by the equation p = ∫ r' ρ(r') dτ'. The integration is performed over the volume that encloses the nonzero charge density ρ(r'). It is established that there is no necessity to integrate over regions of space where the charge density is zero, focusing only on areas with nonzero values. This clarification ensures a more efficient calculation of the dipole moment.

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Wheelwalker
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In "An Introduction to Electrodynamics", Griffiths gives the following equation for the dipole moment: p=\int r' \rho(r') d\tau'. My question is, in general, what volume am I integrating over? It seems a bit arbitrary to me. I assume I'm integrating over whatever volume is enclosing the charge density \rho(r')?
 
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You are summing over all elements of volume ##\small d\tau'## in all of space. However, there is no need to integrate over those parts of space where the integrand is zero. So, you are correct - you only need to integrate over regions where there is some nonzero charge density.
 
That makes sense to me. Thanks!
 

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